Atmospheric predictability research is the basis for weather and climate prediction. Under the background of global warming, meso/micro-scale extreme weather events such as heavy rain and severe convection have occurred more frequently in recent years, and their predictability has attracted wide attention. After briefly reviewing the history of atmospheric predictability research, this paper systematically reviews the latest advances in the predictability of heavy rain and strong convection over the last 20 years (1999–2018). The main research methods for meso/micro-scale predictability and their differences with traditional large-scale weather predictability methods are first discussed. Then, the primary initial error growth mechanism (error upscaling under deep moist convection) is elaborated in detail, and some arguments (error downscaling, error upscaling, and downscaling coexisting) are discussed. The effects of errors in NWP (Numerical Weather Prediction) models and convective environments on the practical predictability are also highlighted, and some recent mesoscale predictability experiments are reviewed. Finally, this paper briefly discusses the current problems, challenges, and future directions of the predictability research of heavy rain and severe convection.